336 إحص: سلاسل زمنية وتنبؤ

Syllabus Description:
Week Subjects
1 Meeting students, Course goals, expected knowledge after completing the course, explain methods of evaluating the student’s performance
Introduction, examples of time series data, goals of time series analysis, measuring forecasting errors, choosing the appropriate method for forecasting, types of change in time series
2 Covariance function, autocorrelation function (importance – estimation), form of the ACF for some cases (nonstationary series, oscillating series, seasonal series), partial autocorrelation function, estimating the PACF
Time series operators (backshift operator, difference operator), using the difference operator for non-stationary series in the mean, variance stabilizing transformations, Box-Cox transformations
3 Stochastic time series models, meaning of linearity in regression models and in time series models, white noise (W.N.) process, stationarity of W.N. process, general linear process, invertibility formula, white noise formula, autoregressive processes (AR), autoregressive process of order one (stationarity condition, ACF, PACF)
AR(2) (stationarity conditions, ACF, PACF), general AR(p), moving average processes (MA), MA(1) (invertibility condition, ACF, PACF)
4 MA(2) (invertibility condition, ACF, PACF), general MA(q), ARMA(p,q) models, ARMA(1,1) model (stationarity condition, invertibility condition ACF, PACF), integrated ARIMA(p,d,q) models
Parameter estimation, moments method, estimating white noise variance, least squares method
5 Forecasting, minimum mean square error forecast, forecasting for AR(1), MA(1), Some results for the general ARMA(p,q), forecast error variance, constructing confidence limits for the forecasts-updating the forecasts
Box-Jenkins methodology, design and construction of forecasting model, model identification, choosing difference order- choosing model order
6 Checking model validity, diagnostics, residual analysis, criteria for choosing the best model (AIC, BIC), analysis of higher (lower) order models
Seasonal models, seasonal autoregressive models, moving average models, Mixed seasonal models, multiplicative seasonal models
7 Leftovers and Review

Textbooks and References:
1. Time Series Analysis with Applications in R, by Jonathan D. Cryer and Kung-Sik Chan, (2008). Springer.
2. The Analysis of Time Series, by C. Chatfield (2003). Chapman and Hall.
3. Introduction to Time Series Analysis and Forecasting, by Douglas G. Montgomery, Cheryl L. Jennings and Murat Kulahci. (2008). Wiley.
4. مقدمة في التحليل الحديث للسلاسل الزمنية. تأليف سمير مصطفى شعراوي. (2005). مركز النشر العلمي، جامعة الملك عبدالعزيز
5. مذكرة الدكتور إبراهيم الواصل
6. مواد أخرى في نظام التعلم الإلكتروني (البلاكبورد)